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Compare the subtraction problems [tex]\left(\frac{6}{8}-\frac{5}{8}=\frac{1}{8}\right)[/tex] and [tex]\left(\frac{6}{9}-\frac{7}{9}=-\frac{1}{9}\right)[/tex]. Why is the answer to the first problem positive and the answer to the second problem negative? Check all that apply.

A. In the second problem, the first fraction is less than the second fraction.
B. The answer to the first problem is positive because the denominator is even.
C. The answer to the second problem is negative because the denominator is odd.
D. If you subtract a lesser number from a greater number, the answer is positive.
E. If you subtract a greater number from a lesser number, the answer is negative.

Sagot :

GinnyAnswer
Let's analyze each statement to understand why the answer to the first problem is positive and the answer to the second problem is negative.

1. In the second problem, the first fraction is less than the second fraction:

The second problem involves the fractions \(\frac{6}{9}\) and \(\frac{7}{9}\). Comparing these fractions, we observe that \(\frac{6}{9}\) is indeed less than \(\frac{7}{9}\). Therefore, this statement is true.

2. The answer to the first problem is positive because the denominator is even:

The first problem involves the subtraction \(\frac{6}{8} - \frac{5}{8}\). Here, the denominator is 8, which is even. However, the reason the answer is positive (\(\frac{1}{8}\)) is not due to the even denominator, but because the numerator after subtraction is positive (\(6 - 5 = 1\)). The evenness of the denominator does not affect the sign of the result in fraction subtraction. Therefore, this statement is false.

3. The answer to the second problem is negative because the denominator is odd:

The second problem involves the subtraction \(\frac{6}{9} - \frac{7}{9}\). Here, the denominator is 9, which is odd. However, the reason the answer is negative (\(-\frac{1}{9}\)) is because the numerator after subtraction is negative (\(6 - 7 = -1\)). The oddness of the denominator does not affect the sign of the result in fraction subtraction. Therefore, this statement is false.

4. If you subtract a lesser number from a greater number, the answer is positive:

In the first problem, \(\frac{6}{8}\) is greater than \(\frac{5}{8}\). Subtracting the lesser number \(\frac{5}{8}\) from the greater number \(\frac{6}{8}\) gives a positive result, \(\frac{1}{8}\). Therefore, this statement is true.

5. If you subtract a greater number from a lesser number, the answer is negative:

In the second problem, \(\frac{6}{9}\) is less than \(\frac{7}{9}\). Subtracting the greater number \(\frac{7}{9}\) from the lesser number \(\frac{6}{9}\) gives a negative result, \(-\frac{1}{9}\). Therefore, this statement is true.

Based on the analysis, the correct statements are:
- In the second problem, the first fraction is less than the second fraction.
- If you subtract a lesser number from a greater number, the answer is positive.
- If you subtract a greater number from a lesser number, the answer is negative.
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